Advantages: Usualy more money, including more money for overtime, possibilities of moving abroad working for different companies. You can claim back on your tax for expenses such as meal allowance, millage allowance, medicals and so on.
Disadvantages: Instability, sometimes you may be promised long term contract but any company financial problems, contractors are the first to go. You have to do your own tax, do not fall into the trap that if you are a contractor you dont pay tax, realisticaly depending on what country you are in, you will be liable to pay tax. The tax man will always come knocking so dont hide. If you have a good accountant it helps. Also think of the possibilities of no pension or possible overlooked for promotion. If your a first officer, you may be overlooked for command even though you have the correct experience, If your a captain you will work hard but will be rewarded financialy which is not a negative. You may not receive certain information from your employer. Most contractor employers promise the world and make you feel very unique but what they promise is sometimes far from what you get. If you get a contract make sure promises are placed in Ink on a contract. There are one or two that you may have to be careful of and there are ones which you dont. Also you may not get holiday pay.
I hope this helps and this is just my opinion, hope you make the right decision and good luck